Nuprl Lemma : pv11_p1_leq_bnum_implies_eq_or_lt
∀ldrs_uid:Id ⟶ ℤ. ∀b1,b2:pv11_p1_Ballot_Num().
(Inj(Id;ℤ;ldrs_uid) ⇒ (↑(pv11_p1_leq_bnum(ldrs_uid) b1 b2)) ⇒ ((b1 = b2 ∈ pv11_p1_Ballot_Num()) ∨ (↑(b1 < b2))))
Proof
Definitions occuring in Statement :
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
inject: Inj(A;B;f),
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
apply: f a,
function: x:A ⟶ B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
all: ∀x:A. B[x],
implies: P ⇒ Q,
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
btrue: tt,
isl: isl(x),
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
pv11_p1_leq_bnum': pv11_p1_leq_bnum'(ldrs_uid),
pv11_p1_lt_bnum': pv11_p1_lt_bnum'(ldrs_uid),
and: P ∧ Q,
or: P ∨ Q,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
rev_implies: P ⇐ Q,
guard: {T},
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
inject: Inj(A;B;f),
le: A ≤ B,
true: True
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b1,b2:pv11\_p1\_Ballot\_Num().
(Inj(Id;\mBbbZ{};ldrs$_{uid}$) {}\mRightarrow{} (\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}\mbackslash{}ff2\000C4) b1 b2)) {}\mRightarrow{} ((b1 = b2) \mvee{} (\muparrow{}(b1 < b2))))
Date html generated:
2016_05_17-PM-03_13_26
Last ObjectModification:
2016_01_18-AM-11_18_53
Theory : paxos!synod
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